That would really restrict what you could buy. I picked up the Amazon Fire TV HDTV and it was on a black friday delivered to my door at about 312USD total. 50 inches but the wired headset seems to drop out so that's a bug. Too bad because so much else works so well. I eventually added a sound bar by Toshiba since Toshiba made the HDTV and to my surprise ARC works correctly. Even controls my BD player.
The Roku just plugs into any HDMI port so that's something all the sets have.
As to the battery time, no HDTV I know comes with wireless headsets so the time on battery is something you check into on its own.
-> So what next? Make a list of 400 to 500 buck models then check to see if they have the headphone jack and mention Bluetooth headphone support. You won't find many.
If you don't want to do that work, just go to Bestbuy and tell them your requirements. Get the model numbers and check again they have the required features.
Sadly I have yet to find a HDTV finder/shopper that does this for us.
So the market is flooded with so many darn tv's it's mind boggling. What I'm looking for:
At least 50 inch if possible
$400 - $500
Smart TV
More than one USB port
More than one HDMI port
WiFi since I assume this would be my only option with my computer and router in another room?
Able to hook up Roku in the future
Able to hook up both wired and wireless headphones. If this is even possible. As I am disabled, watch a lot of tv and have weird sleep schedule. so need to be sure that if I'm watching really late (or just want that extra volume) I can listen with headphones but not worry if the batteries go dead. And the least amount of time I can get away without a cord the better, since one of my little ****** cats likes chewing on wires.
And any other features that would be beneficial.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic